SOLUTION: Mark Martin can row upstream at 5mph and downstream at 11mph. If Mark starts rowing upstream until he gets tired and then rows downstream to his starting point, hhow far did Mark r

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Question 236019: Mark Martin can row upstream at 5mph and downstream at 11mph. If Mark starts rowing upstream until he gets tired and then rows downstream to his starting point, hhow far did Mark row if the entire trip took 4 hours?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Write a separate equation for each
part of the trip
upstream:
d%5B1%5D+=+r%5B1%5D%2At%5B1%5D
(1) d%5B1%5D+=+5%2At%5B1%5D mi
downstream:
d%5B2%5D+=+r%5B2%5D%2At%5B2%5D
(2) d%5B2%5D+=+11%2At%5B2%5D mi
also:
d%5B1%5D+=+d%5B2%5D (I'll call them both d)
t%5B1%5D+%2B+t%5B2%5D+=+4 hrs
t%5B2%5D+=+4+-+t%5B1%5D hrs
--------------------------
(1) d+=+5t%5B1%5D
(2) d+=+11%2A%284+-+t%5B1%5D%29
(2) d+=+44+-+11t%5B1%5D
Subtract (1) from (2)
0+=+44+-+11t%5B1%5D+-+5t%5B1%5D
11t%5B1%5D+%2B+5t%5B1%5D+=+44
16t%5B1%5D+=+44
t%5B1%5D+=+2.75 hrs
and, since
t%5B2%5D+=+4+-+t%5B1%5D
t%5B2%5D+=+4+-+2.75
t%5B2%5D+=+1.25
-----------------------
(1) d%5B1%5D+=+5%2At%5B1%5D
d%5B1%5D+=+5%2A2.75
d%5B1%5D+=+13.75 mi
and
d%5B2%5D+=+11%2At%5B2%5D
d%5B2%5D+=+11%2A1.25
d%5B2%5D+=+13.75 mi
Both distances are the same, as they should be
Mark rowed 13.75+%2B+13.75+=+27.5 mi